DE-BUNDESWETTBEWERB 2005 Problem 6

Round 2

Let be $x$ a rational number. Prove: There are only finitely many triples $(a,b,c)$ of integers with $a<0$ and $b^2-4ac=5$ such that $ax^2+bx+c$ is positive.

Dataset text AI-MO AoPS. Quoted with source.

Official text: Bundeswettbewerb Mathematik 2005 official paper, page 1.

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